Question

the area of right triangle efg is 49 square inches.

Explanation:

Step1: Recall area formula for triangle

The area formula for a right - triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. Here, $b = 14$ inches and $h=x + 4$ inches, and $A = 49$ square inches. So we have the equation $\frac{1}{2}(14)(x + 4)=49$.

Step2: Simplify the left - hand side of the equation

First, simplify $\frac{1}{2}(14)(x + 4)$. $\frac{1}{2}\times14=7$, so the equation becomes $7(x + 4)=49$.

Step3: Distribute the 7

Using the distributive property $a(b + c)=ab+ac$, we get $7x+28 = 49$.

Step4: Solve for x

Subtract 28 from both sides of the equation: $7x+28-28=49 - 28$, which simplifies to $7x=21$. Then divide both sides by 7: $\frac{7x}{7}=\frac{21}{7}$, so $x = 3$.

Answer:

$x = 3$