Question

Write an expression for the area of the figure shown above

Answer 1

`\red{ \bold{ 7 {x}^(2) + 180x + 324 = 0}}`

Explanation:

Given is an isosceles right triangle.

Therefore, by Pythagoras theorem:

`{(5x + 18)}^(2) = {( - 3x)}^(2) + {( - 3x)}^(2) \\ \\ \implies \: {(5x)}^(2) + 2(5x)(18) + {(18)}^(2) = 9 {x}^(2) + 9 {x}^(2) \\ \\ \implies \: 25 {x}^(2) + 180x + 324 = 18 {x}^(2) \\ \\ \implies \: 25 {x}^(2) - 18 {x}^(2) + 180x + 324 = 0 \\ \\ \implies \: \ \red{ \bold{ 7 {x}^(2) + 180x + 324 = 0}}\\ \\`