Bonnie planted a garden in her backyard. Both the garden and the backyard are right triangles. The garden is proportional to the backyard. The garden has dimensions of 6, 8 and 10 yards. What is the area of Bonnie's backyard if its hypotenuse is 30 yards?

Question

Mathematics

Byron Davenport

31 August, 16:58

Bonnie planted a garden in her backyard. Both the garden and the backyard are right triangles. The garden is proportional to the backyard. The garden has dimensions of 6, 8 and 10 yards. What is the area of Bonnie's backyard if its hypotenuse is 30 yards?

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Amanda · Answer 1

You can find the area of Bonnue's backyard by comparing the hypotenuse of the garden to the hypotenuse of the back yard. If the hypotenuse of the garden is 10 (with the side lengths being 6, 8 and 10 - the longest is always the hypotenuse) and the hypotenuse of the back yard is 30, this is a scale factor of 3 (3 times longer).

This means the other two sides would also be 3 times longer.

6 yards x 3 = 18

8 yards x 3 = 24

To find the area using these dimensions, you will use the formula for finding the area of a triangle.

A = 1/2bh

A = 1/2 x 18 x 24

A = 216 square yards

The area of the backyard is 216 square yards.