a-piece-of-wire-40cm-long-is-cut-into-two-parts-and-each-part-is-then-bent-into-a-square-if-the-sum-of-these-squares-is-68cm-2-find-the-lengths-of-the-two-pieces-of-wire-

Question Number 40764 by mondodotto@gmail.com last updated on 27/Jul/18

a piece of wire 40 cm long

is cut into two parts and each part

is then bent into a square . if the sum

of these squares is 68 {cm}^{2}

find the lengths of the two

pieces of wire .

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Jul/18

x = 4 a_{1} 40 - x = 4 a_{2}

a_{1}^{2} + a_{2}^{2} = 68

4 a_{1} + 4 a_{2} = 40

a_{1}^{2} + {(10 - a_{1})}^{2} = 68

2 a_{1}^{2} - 20 a_{1} + 32 = 0

a_{1}^{2} - 10 a_{1} + 16 = 0

(a_{1} - 2) (a_{1} - 8) = 0

i f a_{1} = 2 a_{2} = 8

i f a_{1} = 8 a_{2} = 2

l e n t t h o f t w o p i e c e a r e 4 \times 2 a n d 4 \times 8

8 c m a n d 32 c m