Question

the shorter sides of an acute triangle are x cm and 2x cm. the longest side of the triangle is 15 cm. what is the smallest possible whole - number value of x? 6 7 8 9

Explanation:

Step1: Apply triangle inequality

For a triangle with sides $x$, $2x$, $15$, the sum of shorter sides must exceed the longest side:
$x + 2x > 15$
$3x > 15$
$x > 5$

Step2: Apply acute triangle condition

For an acute triangle, the square of the longest side must be less than the sum of squares of the other two sides:
$15^2 < x^2 + (2x)^2$
$225 < x^2 + 4x^2$
$225 < 5x^2$

Step3: Solve the inequality

Divide both sides by 5:
$\frac{225}{5} < x^2$
$45 < x^2$
Take square root:
$x > \sqrt{45} \approx 6.708$

Step4: Find smallest whole number

Since $x$ must be an integer greater than 6.708, the smallest value is 7.

Answer:

B. 7