Question

The diagonal of a rectangular field exceeds its length by 2 m and exceeds
twice its breadth by 1 m. Find the length and breadth of the field.​

Answer 1

Answer:

Using the Pythagorean Theorem which applies to right triangles:

(a)2 + (b)2 = (c)2

meaning a-squared + b-squared = c-squared

Where a is the length of the width

b is the length of the side and

c is the length of the diagonal

Now since the diagonal exceeds the length by 2cm, we will rewrite the diagonal as

(b + 2) or (side + 2)

Now let's fill in the blanks

(10)2 + (b)2 = (b+2)2

Simplifying gives us:

100 +(b)2 = (b)2 + 4b + 4

subtracting (b)2 from both sides gives us

100 = 4b + 4

subtracting 4 gives us

96 = 4b

divididing by 4 gives us

24 = b

length = 24

diagonal = 24 + 2 = 26

Checking our work to show it's correct gives us

(10)2 + (24)2 = (26)2

100 + 576 = 676