Rearrange formulas to isolate specific variables | Linear equations | Algebra I | Khan Academy

The formula for the face of a triangle is: A = 1/2 bh, where A is the face, b is the length of the base, and h is the height. The face is equal to 1/2 the length of the base along the length of the height. Find a height formula. Let me draw a triangle. We know what b and h are. b is the base, here is the length here. And the length here is h – the height, which I denote by h. We have to write a formula for h, starting from the formula A = (bh) / 2 We are looking for the formula for h. That is, h should be equal to something, be on one of the two sides of the equation. It’s already on the right, so let’s remove what’s also on the right. Let’s do it step by step … Let’s see if we can move 1/2. We could multiply each of the sides by the reciprocal of 1/2, ie. by 2/1. Which is 2. Let’s multiply by 2. I put * 2 on the left and right. The idea is that 1/2 by 2 is equal to 1. And so the right side will become bh. And the left side becomes 2A. We are almost ready. We have b multiplied by h. To leave h only, we divide each of the two sides of the equation by b. B / b is abbreviated on the right and on the right we get 2A / b. And so we got h = 2A / b And we are ready! We found the formula for h using the formula for A. This is useful for a task in which we have different triangles, with different heights and faces, which are given to us, but ask us what their heights are.