Given the area of the triangle exceeding the area of the rectangle by 39cm². compute the perimeter of the two diagrams.

Perimeter or square = 12cm

Perimeter of triangle = 32cm

Step-by-step explanation:

Since the rectangle's length and breadth are equal, it must be a square.

So,

area of the triangle = area of square

(1/2) × base × height = 39 + length ^ 2

(1/2) × 4y × ( y + 5 ) = 39 + y^2

(1/2) ( 4y^2 + 20y ) = 39 + y^2

2y^2 + 10y = 39 + y^2

y^2 + 10y - 39 = 0

y^2 - 3y + 13y - 39 = 0

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

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

So, y = 3.

Now,

Perimeter or square = 4 × length

= 4 × 3

= 12 cm

Calculate side of a triangle by using Pythagoras theorem.

Perimeter of triangle = 2 × sides + 4y

= 2 × 10 + 4 × 3

= 32 cm

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