Geometry — Daily Practice

Monday, July 20, 2026 · 5 problems · Best Math Resources

1.Geometry · Pythagorean theorem
A right triangle has legs of length $6$ and $8$ . Find the length of the hypotenuse.
2.Geometry · Pythagorean theorem
Sir Reginald the Squirrel is stuck at the bottom of a giant oak tree, clutching an acorn the size of his own head. His nut-stash is up in a hollow that is $12$ meters straight up the trunk. But Sir Reginald refuses to climb straight up (too mainstream), so he takes his patented 'Diagonal Dash' along a perfectly straight ramp. The base of the ramp starts $5$ meters away from the trunk on the ground. If the ground, the trunk, and the ramp form a right triangle, how long is Sir Reginald's diagonal ramp $c$ (in meters)?
3.Geometry · Pythagorean theorem
A right triangle has legs measuring $9$ units and $12$ units. Find the length of the hypotenuse.
4.Geometry · Area of rectangles
A rectangle has a length of $15$ meters and a width of $8$ meters. Find its area in square meters.
5.Geometry · Perimeter
A rectangle has a length of $12$ cm and a width of $7$ cm. Find the perimeter of the rectangle.

Solutions

Geometry · Monday, July 20, 2026

1.Geometry · Pythagorean theorem
A right triangle has legs of length $6$ and $8$ . Find the length of the hypotenuse.
1. By the Pythagorean theorem, $c^2 = a^2 + b^2$ .
2. Substitute the leg lengths: $c^2 = 6^2 + 8^2$ .
3. Compute the squares: $c^2 = 36 + 64 = 100$ .
4. Take the square root: $c = \sqrt{100} = 10$ .
Answer:
$10$
2.Geometry · Pythagorean theorem
Sir Reginald the Squirrel is stuck at the bottom of a giant oak tree, clutching an acorn the size of his own head. His nut-stash is up in a hollow that is $12$ meters straight up the trunk. But Sir Reginald refuses to climb straight up (too mainstream), so he takes his patented 'Diagonal Dash' along a perfectly straight ramp. The base of the ramp starts $5$ meters away from the trunk on the ground. If the ground, the trunk, and the ramp form a right triangle, how long is Sir Reginald's diagonal ramp $c$ (in meters)?
1. The trunk (height) and the ground distance are the two legs of a right triangle: $a = 5$ and $b = 12$ .
2. By the Pythagorean theorem, $c^2 = a^2 + b^2$ .
3. Substitute: $c^2 = 5^2 + 12^2 = 25 + 144 = 169$ .
4. Take the positive square root: $c = \sqrt{169} = 13$ .
Answer:
$c = 13 \text{ meters}$
3.Geometry · Pythagorean theorem
A right triangle has legs measuring $9$ units and $12$ units. Find the length of the hypotenuse.
1. The Pythagorean theorem states that for a right triangle with legs $a$ and $b$ and hypotenuse $c$ : $a^2 + b^2 = c^2$ .
2. Substitute the given leg lengths: $c^2 = 9^2 + 12^2$ .
3. Compute the squares: $c^2 = 81 + 144 = 225$ .
4. Take the square root of both sides: $c = \sqrt{225} = 15$ .
Answer:
$c = 15$ units
4.Geometry · Area of rectangles
A rectangle has a length of $15$ meters and a width of $8$ meters. Find its area in square meters.
1. The area of a rectangle is given by the formula $A = \text{length} \times \text{width}$ .
2. Substitute the given values: $A = 15 \times 8$ .
3. Multiply: $A = 120$ square meters.
Answer:
$120 \text{ m}^2$
5.Geometry · Perimeter
A rectangle has a length of $12$ cm and a width of $7$ cm. Find the perimeter of the rectangle.
1. The perimeter of a rectangle is given by $P = 2(l + w)$ .
2. Substitute $l = 12$ and $w = 7$ : $P = 2(12 + 7)$ .
3. Simplify inside the parentheses: $P = 2(19)$ .
4. Multiply: $P = 38$ cm.
Answer:
$P = 38$ cm