Question

The area of a triangle is 30cmsquare find the base if the altitude exceeds the base by 7 cm​

Answer 1

5 cm

Explanation:

Area= 1/2 base×altitude

let base be x cm hence altitude = x+7 cm

30 = 1/2 (x) (x+7)

60= x^2 + 7x

x = 5 or - 12

but measurements can't be in negative form hence -12 is discarded. Thus x= 5 cm

x= base hence base = 5cm

Answer 2

base = 5 cm

Explanation:

The area (A) of a triangle is calculated as

A =
`(1)/(2)` bh ( b is the base and h the altitude )

let base be b then h = b + 7

Given A = 30, then

`(1)/(2)`b(b + 7) = 30 ( multiply both sides by 2 to clear the fraction )

b(b + 7) = 60 ← distribute left side

b² + 7 = 60 ( subtract 60 from both sides )

b² + 7 - 60 = 0 ← in standard form

(b + 12)(b - 5) = 0 ← in factored form

Equate each factor to zero and solve for b

b + 12 = 0 ⇒ b = - 12

b - 5 = 0 ⇒ b = 5

However, b > 0, thus b = 5

That is the base is 5 cm