The base of a triangle is 4 cm greater than the height the area is 30 cm² find the height and the length of the base

Answer 1

The area of a triangle, being half that of a rectangle, is 1/2(base x height). Using h for height, and b for base, we know that b=h+4. Substitute (h+4) for b in the formula to get

30 = 1/2 h(h+4)

Multiply both sides by 2: 60 = h(h+4).

Use the distributive property on the right side: 60 = h²+4h.

Subtract 60 from both sides: 0 = h²+4h-60.

Factor to solve: 0 = (h-6)(h+10)

h= -10, 6.

We can't have a negative height, so h = 6cm.

The base is h+4, so b = 10cm.

I hope this helps; let me know if you have any more questions, and have fun mathing!

Liz Z.