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: $b=\dfrac{2A-(p+q)L}{h}$

Step-by-step 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 :

$A=\dfrac{1}{2}bh+\dfrac{1}{2}(p+q)L$

, 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$\dfrac{1}{3}(p+q)L$ from both sides of the given formula , we get

$A-\dfrac{1}{2}(p+q)L=\dfrac{1}{2}bh$

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

$\dfrac{2}{h}(A-\dfrac{1}{2}(p+q)L)=b\\\\\Rightarrow\ b=\dfrac{1}{h}(2A-(p+q)L)$

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 :-

$b=\dfrac{2A-(p+q)L}{h}$