Question

Find the edges of rectangular
Solid whose diagonal is 13cm
Volume is 144 m3 and the
area of the base is 48 cm²​

Answer 1

Answer:

the edges of rectangular solid are 12 cm 4 cm and 3 cm

Step-by-step explanation:

Probably the volume should be 144 cm^3

let us assume the edges of the rectangular solid  a , b , c as length , width & height respectively .

so the diagonal of the rectangular solid = $\sqrt{} a^{2} +b^{2} + c^2$ = 13 cm →(1)

volume = a × b × c =  144 cm^3 →(2)

area of base = a × b = 48 cm^2 →(3)

by (2) ÷ (3) we get $\frac{a b c}{ab}$ = c = 144/48 = 3 cm ⇒ c = 3 cm →(4)

from (1) we get , $a^{2} + b^{2} + c^{2}$ = 13^2 = 169 →(5)

now putting the value of c = 3 cm in equation (5) we get , $a^{2} + b^{2} + 9 = 169$

⇒ $a^{2} +b^{2}$ = 160 →(6)

now, from (6) & (3) , $a^{2} + b^{2} + 2ab$ = 160 + (2×48) = 160 + 96 = 256

⇒ $(a+b)^{2}$ = 256

⇒ a+ b = $\sqrt{256}$ = 16 →(7)

again from (6) & (3) , $a^{2} + b^{2} - 2ab$ = 160 - (2×48) = 160 - 96 = 64

⇒ $(a-b)^{2}$ = 64

⇒ a - b = $\sqrt{64}$ = 8 →(8)

by (7) + (8) ,

2a = 24 ⇒ a = 12

by (7) - (8) ,

2b = 8 ⇒ b = 4

Hence required values , a = 12 cm , b = 4 cm & c = 3 cm