Question Solve for $h$ in the equation $2(15)(85)+2(10)(65)=2(9 \sqrt{8}) h$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $(15)(85)+(10)(65)=(9 \sqrt{8}) h$ . We are asked to solve for $h$

STEP 2

First, let's simplify the left side of the equation.
$2(15)(85)+2(10)(65)$

STEP 3

Calculate the multiplication in the brackets.
$2 \times1275 +2 \times650$

STEP 4

Perform the multiplication.
$2550 +1300$

STEP 5

Add the two values together.
$3850$ So, the left side of the equation simplifies to3850.

STEP 6

Now, let's simplify the right side of the equation.
$2(9 \sqrt{8}) h$

STEP 7

Calculate the multiplication in the brackets.
$2 \times9 \times \sqrt{} \times h$

STEP 8

Perform the multiplication.
$18 \sqrt{8} h$ So, the right side of the equation simplifies to $18 \sqrt{8} h$ .

STEP 9

Now, we can rewrite the equation with the simplified left and right sides.
$385 =18 \sqrt{8} h$

STEP 10

To solve for $h$ , we need to isolate $h$ on one side of the equation. We can do this by dividing both sides of the equation by $18 \sqrt{8}$ .
$h = \frac{3850}{18 \sqrt{8}}$

STEP 11

implify the right side of the equation.
$h = \frac{3850}{18 \times \sqrt{}}$

STEP 12

Perform the multiplication in the denominator.
$h = \frac{3850}{36 \sqrt{2}}$

STEP 13

To rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{2}$ .
$h = \frac{3850 \sqrt{2}}{36 \times2}$

STEP 14

Perform the multiplication in the denominator.
$h = \frac{3850 \sqrt{2}}{72}$ So, the solution to the equation is $h = \frac{3850 \sqrt{2}}{72}$ .

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