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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Here are the solutions to the problems: Question 34a: The triangle has sides (x-5) cm, 2x cm, and 2x cm (indicated by the dash marks). The perimeter is 40 cm. Step 1: Write the equation for the perimeter. The perimeter is the sum of all sides. (x-5) + 2x + 2x = 40 Step 2: Combine like terms. (x + 2x + 2x) - 5 = 40 5x - 5 = 40 Step 3: Solve for x. Add 5 to both sides: 5x = 40 + 5 5x = 45 Divide by 5: x = (45)/(5) x = 9 Step 4: Calculate the length of each side. Side 1: x-5 = 9-5 = 4 cm Side 2: 2x = 2(9) = 18 cm Side 3: 2x = 2(9) = 18 cm The lengths of the sides of the triangle are 4 cm, 18 cm, and 18 cm. 4 cm, 18 cm, 18 cm Question B: The length of a rectangle is twice the width. The perimeter is 48 cm. Step 1: Define variables and set up equations. Let the width be w. Let the length be l. Given: l = 2w The formula for the perimeter of a rectangle is P = 2(l+w). Given: P = 48 cm. Step 2: Substitute the given information into the perimeter formula. 48 = 2(2w + w) Step 3: Simplify and solve for w. 48 = 2(3w) 48 = 6w Divide by 6: w = (48)/(6) w = 8 The width of the rectangle is 8 cm. 8 cm Question C: Jum has some money. Leo has twice as much as Jum. Their total sum of money is 750. Step 1: Define variables and set up equations. Let Jum's money be J. Let Leo's money be L. Given: L = 2J Given: J + L = 750 Step 2: Substitute the expression for L into the total sum equation. J + 2J = 750 Step 3: Solve for J. 3J = 750 Divide by 3: J = (750)/(3) J = 250 So, Jum has 250. Step 4: Calculate Leo's money. L = 2J L = 2(250) L = 500 Leo has 500. 500 Send me the next one 📸