MATHEMATICS HIGH SCHOOL

The base of a triangle is 3 cm longer than its altitude. The area of the triangle is 35cm^2. Find the altitude. (Hint: use the area of a triangle. 1/2 * base * altitude.)

Answers

Answer 1
Answer:

The altitude of the triangle whose base is 3 cm longer than its altitude is 7cm.

What is triangle?

Triangle is a plane figure with three straight sides and three angles such that the sum of the angles is 180°.

Given is a triangle whose base is 3cm longer than its altitude. The area of the triangle is 35 cm².

Assume that the altitude of the triangle is 'a' cm.

The area of a tringle is given by -

A [T] = 1/2 x base x height.

Now,

Altitude of triangle = a cm

Base of triangle = (a + 3) cm

Substituting the values in the formula of area, we get -

A [T] = 1/2 x base x height

A [T] = 1/2 x a x (a + 3)

a(a + 3) = 35 x 2

a(a + 3) = 70

a² + 3a - 70 = 0

On solving the above quadratic equation, you will get two values of x -

a = - 10   and   a = 7

Altitude cannot be negative. Therefore, the altitude of the triangle is 7 cm.

Therefore, the altitude of the triangle whose base is 3 cm longer than its altitude is 7cm.

To solve more questions on tringles, visit the link below-

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Answer 2
Answer: The base is 3+(x), altitude is x so substitute. Now we know the area of a triangle is base X height X 1/2. Substitute again! 1/2 (3+x)(x)=35. Multiply both sides by 2 to cancel out the 1/2. Now you have (x)(x+3)=70 and you have to foil out the left side x^2+3x=70. Subtract 70 on both sides x^2+3x-70=0. Find two numbers that multiply to -70 and add to 3. Solve (x+10)(x-7)=0. the x value is 7. since you can't have negative length values. Substitute 7 into 3+x for the base so you know the base is 10 and the height is 7.

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Answer:

1

Step-by-step explanation:

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Answers

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