Atriangle is 5 cm wider than it is tall. the area is 52 cm^2 . find the height and the base .

8 cm and 13 cm

Step-by-step explanation:

The formula to calculate the area (A) of a triangle is

A = bh ( b is the base and h the height )

let height = h then base = h + 5 ( base is 5 cm wider than it is tall ), hence

A = h(h + 5) = 52

multiply both sides by 2

h(h + 5) = 104 ( rearrange into standard form )

h² + 5h - 104 = 0 ← in standard form

(h + 13)(h - 8) = 0 ← in factored form

equate each factor to zero and solve for h

h + 13 = 0 ⇒ h = - 13

h - 8 = 0 ⇒ h = 8

but h > 0 ⇒ h = 8

Thus the height = 8 cm and base = 8 + 5 = 13 cm

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step-by-step explanation:

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