Question

Diagram 1 shows a triangle with feet of length 4y cm and height (y + 5) cm. Diagram 2 shows a square with a length of y cm. Given the area of ​​the triangle exceeds the rectangle by 39 cm². Calculate the perimeter of the two diagrams.​

Answer 1

Explanation:

Diagram 1

Area = b*h/2 = 4y*(y+5)/2 = 2y*(y+5)= 2y² + 10y

Diagram 2

Area = side*side = y * y = y²

the area of ​​the triangle exceeds the rectangle by 39 cm².

2y² + 10y - y² = 39

y² + 10y = 39

y² + 10y -39 = 0

y² +13y - 3y - 3*13 = 0

y(y+13) -3(y+13)=0

(y+13)(y-3) = 0

y + 13 = 0 will not come as length couldn't be in negative

y - 3 = 0

y = 3 cm

Diagram 2:

Perimeter = 4*side = 4*y = 4*3 = 12 cm