Chapter 5: Q19 (page 187)

$\bar{GM}$ is a median of right $Δ IRG$
If $GM = 2 y + 3$ and $RI = 12 - 8 y$ find the value of y.

Short Answer

Expert verified

The value of y is $\frac{1}{2}$ .

Step by step solution

Step 1. Description of step.

For the right-angled triangle, the median is half of the hypotenuse.

Therefore, $G M = \frac{R I}{2}$ .

Step 2. Description of step.

Substitute $2 y + 3$ for $G M$ and $12 - 8 y$ for $R I$ into $G M = \frac{R I}{2}$ .

$\begin{matrix} 2 y + 3 = \frac{12 - 8 y}{2} \\ 2 (2 y + 3) = 12 - 8 y \\ 4 y + 6 = 12 - 8 y \\ 12 y = 6 \end{matrix}$

Step 3. Description of step.

Divide each side of the obtained equation in steps 2 by 6 to find the value of y.

$\begin{matrix} \frac{12 y}{12} = \frac{6}{12} \\ y = \frac{1}{2} \end{matrix}$

Therefore, the value of y is $\frac{1}{2}$ .

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$\bar{GM}$ is a median of right $Δ IRG$
If $GM = 2 y + 3$ and $RI = 12 - 8 y$ find the value of y.

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

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GM¯is a median of right ΔIRGIf GM=2y+3and RI=12-8yfind the value of y.

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

One App. One Place for Learning.

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$\bar{GM}$ is a median of right $Δ IRG$
If $GM = 2 y + 3$ and $RI = 12 - 8 y$ find the value of y.