Question

1. The Kahn's Family lives in a house that has a backyard in the shape of an isosceles trapezoid and a triangle. The area of the backyard can be expressed as the sum of the area of the triangle and the area of the trapezoid, which is bh+(pq The base and the height of the triangle are represented by b and h, respectively. The bases of the trapezoid are p and q, and the height of the trapezoid is L. 2 Rearrange the formula to find the length of base as a function of the lengths of the other sections of the backyard.

Answer 1

Answer:
`b=(2A-(p+q)L)/(h)`

Explanation:

Given : The Kahn's Family lives in a house that has a backyard in the shape of an isosceles trapezoid and a triangle.

The area (A) of the backyard can be expressed as the sum of the area of the triangle and the area of the trapezoid :

`A=(1)/(2)bh+(1)/(2)(p+q)L`

, where base and the height of the triangle are represented by b and h, respectively. The bases of the trapezoid are p and q, and the height of the trapezoid is L.

To find the formula for base b, we subtract expression
`(1)/(3)(p+q)L` from both sides of the given formula , we get

`A-(1)/(2)(p+q)L=(1)/(2)bh`

Now, multiply both sides by 2 and divide both sides by h , we get

`(2)/(h)(A-(1)/(2)(p+q)L)=b\\\\\Rightarrow\ b=(1)/(h)(2A-(p+q)L)`

i.e. The formula to find the length of base as a function of the lengths of the other sections of the backyard will be :-

`b=(2A-(p+q)L)/(h)`