This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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+ 2x + 5 40 = 4x - 5 Step 3: Solve for x. 40 + 5 = 4x 45 = 4x x = (45)/(4) x = 11.25 Step 4: Calculate the length of each side. Side 1: x - 5 = 11.25 - 5 = 6.25 cm Side 2: x - 5 = 11.25 - 5 = 6.25 cm Side 3: 2x + 5 = 2(11.25) + 5 = 22.5 + 5 = 27.5 cm The lengths of the sides of the triangle are 6.25 cm, 6.25 cm, and 27.5 cm. B. Step 1: Let the width of the rectangle be w. Step 2: The length l is twice the width, so l = 2w. Step 3: The perimeter P of a rectangle is given by P = 2(l + w). Substitute the given perimeter and expressions for length and width: 48 = 2(2w + w) 48 = 2(3w) 48 = 6w Step 4: Solve for w. w = (48)/(6) w = 8 The width of the rectangle is 8 cm. C. Step 1: Let Juzi's money be y. Step 2: Leo has twice as much as Juzi, so Leo has 2y. Step 3: Their total sum of money is 750. y + 2y = 750 3y = 750 Step 4: Solve for y. y = (750)/(3) y = 250 Step 5: Calculate how much Leo has. Leo has 2y = 2 × 250 = 500. Leo has sh. 500. That's 2 down. 3 left today — send the next one.