Question

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

Answer 1

The height and base of the triangle are determined using the area formula of a triangle, setting up a quadratic equation with the given conditions, and solving for the height first, then the base.

Step-by-step explanation:

To solve for the height and base of the triangle given that the area is 52 cm2 and the base is 5 cm wider than the height, we can set up an equation using the area formula of a triangle, which is Area = 1/2 × base × height. Let the height of the triangle be h cm, then the base will be h + 5 cm. Substituting the values, we get:

52 = 1/2 × (h + 5) × h

By rearranging and simplifying this equation, we obtain a quadratic equation in terms of h. Solving this quadratic equation will yield the height of the triangle, and then we can easily find the base by adding 5 cm to the height value.

Answer 2

8 cm and 13 cm

Step-by-step explanation:

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

A =
`(1)/(2)` 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 =
`(1)/(2)` 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