Question

Corey is designing a rectangular garden. the garden's diagonal must be 15.6 feet, and the ratio between the garden's base and height must be 12 : 5. find the length of the garden's base and height.

Answer 1

The base of the garden is 14.4 feet.

The height of the garden is 6 feet.

Given,

Corey is designing a rectangular garden;

The diagonal of the garden = 15.6 feet

Ratio  between garden's base and height = 12:5

We have to find the length of base and height of the garden.

Here,

Diagonal of a rectangle, d = $\sqrt{base^{2}+ height^{2} }$

Base = 12x

Height = 5x

Then,

Diagonal, 15.6 = $\sqrt{(12x)^{2} + (5x)^{2} }$

15.6 = $\sqrt{144x^{2} +25x^{2} }$

15.6 = √169x²

15.6 = 13 √x²

15.6 = 13x

x = 15.6/13

x = 1.2

Then,

Base of the garden = 12 x 1.2 = 14.4 feet

Height of the garden = 5 x 1.2 = 6 feet

Learn more about diagonal of a rectangle here;

brainly.com/question/22530917

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